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Modern Geometry— Methods and Applications

Part II: The Geometry and Topology of Manifolds

  • B. A. Dubrovin
  • S. P. Novikov
  • A. T. Fomenko

Part of the Graduate Texts in Mathematics book series (GTM, volume 104)

Table of contents

  1. Front Matter
    Pages i-xv
  2. B. A. Dubrovin, S. P. Novikov, A. T. Fomenko
    Pages 1-64
  3. B. A. Dubrovin, S. P. Novikov, A. T. Fomenko
    Pages 99-134
  4. B. A. Dubrovin, S. P. Novikov, A. T. Fomenko
    Pages 185-219
  5. B. A. Dubrovin, S. P. Novikov, A. T. Fomenko
    Pages 220-296
  6. B. A. Dubrovin, S. P. Novikov, A. T. Fomenko
    Pages 297-357
  7. B. A. Dubrovin, S. P. Novikov, A. T. Fomenko
    Pages 358-418
  8. Back Matter
    Pages 419-432

About this book

Introduction

Up until recently, Riemannian geometry and basic topology were not included, even by departments or faculties of mathematics, as compulsory subjects in a university-level mathematical education. The standard courses in the classical differential geometry of curves and surfaces which were given instead (and still are given in some places) have come gradually to be viewed as anachronisms. However, there has been hitherto no unanimous agreement as to exactly how such courses should be brought up to date, that is to say, which parts of modern geometry should be regarded as absolutely essential to a modern mathematical education, and what might be the appropriate level of abstractness of their exposition. The task of designing a modernized course in geometry was begun in 1971 in the mechanics division of the Faculty of Mechanics and Mathematics of Moscow State University. The subject-matter and level of abstractness of its exposition were dictated by the view that, in addition to the geometry of curves and surfaces, the following topics are certainly useful in the various areas of application of mathematics (especially in elasticity and relativity, to name but two), and are therefore essential: the theory of tensors (including covariant differentiation of them); Riemannian curvature; geodesics and the calculus of variations (including the conservation laws and Hamiltonian formalism); the particular case of skew-symmetric tensors (i. e.

Keywords

Applications Lie group Linking coefficient Riemannian geometry curvature differential geometry foliation manifold

Authors and affiliations

  • B. A. Dubrovin
    • 1
  • S. P. Novikov
    • 2
  • A. T. Fomenko
    • 3
  1. 1.Department of Mathematics and MechanicsMoscow UniversityMoscowRussia
  2. 2.Institute of Physical Sciences and TechnologyMaryland UniversityCollege ParkUSA
  3. 3.Moscow State UniversityMoscowRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-1100-6
  • Copyright Information Springer-Verlag New York Inc. 1985
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-7011-9
  • Online ISBN 978-1-4612-1100-6
  • Series Print ISSN 0072-5285
  • Buy this book on publisher's site